Continuous Logical Modeling of the Submergence...

Philippine Journal of Science146 (1): 15-26, March 2017ISSN 0031 - 7683Date Received: ?? Feb 20??

Key words: continuous logical model, ethylene, hormone crosstalk, submergence

Continuous Logical Modeling of the Submergence Regulatory Network in Rice

1Institute of Mathematical Sciences and Physics University of the Philippines Los Baños, Laguna, Philippines

2Institute of Biological Sciences University of the Philippines Los Baños, Laguna, Philippines

3Department of Membrane Biochemistry Max Planck Institute of Biochemistry, Martinsried, Germany

*Corresponding author: [email protected]

Allen L. Nazareno1*, Maribel L. Dionisio-Sese2, Genaro A. Cuaresma1,

Eduardo R. Mendoza1,3 and Editha C. Jose1

The study on the interaction of different hormones involved in plant developmental processes under environmental stresses is an important area of concern in systems biology. With this, a detailed network structure of submergence regulatory system in rice (Oryza sativa L.) was analyzed using continuous logical modeling. The model correctly simulated the functioning of core components of the network. Moreover, it showed oscillatory behavior of majority of the components, which is consistent with the notion of inherent buffering in signaling networks. A prediction of the role of SUBMERGENCE 1A (SUB1A) in sustained oscillatory behavior of ethylene during submergence in water was also established.

INTRODUCTIONStudying plant hormones has been an emerging trend in systems biology. Plant hormones or phytohormones are generally defined as low molecular mass substances, which, in very dilute concentrations and without being altered chemically, perform specific regulatory functions usually beyond the individual cell. They are responsible for plant's metabolic homeostasis and developmental stability. Specifically, they function as transportable messenger substances and as indigenous signal transmitters (Mohr & Schopfer 1995). Their mechanism of action and the underlying processes related therein have aroused the interest of a vast number of biologists, chemists and even mathematicians.

Crosstalk or the study on the interaction of different hormones involved in plant developmental processes, especially under various environmental influences, has been an emerging field of study in plant phsiology. Kohli & Screenivasulu (2013) indicated the central role of phytohormone crosstalk in regulating growth responses under stress. In addition, the interactions among phytohormones are responsible for controlling input signal and growth responses and in acquiring stress tolerance. Various reviews and researches about the mechanisms of signaling crosstalk were published (Arc et al. 2013; Golldack et al. 2013; Kohli & Screenivasulu 2013; Wang et al. 2013). Many researches on the interactions of different phytohormones, such as gibberellin (GA), abscisic acid (ABA), and ethylene (ET), relative to water submergence stress, particularly in rice, have also been reported (Perata & Voesenek 2007; Fukao & Bailey-Serres 2008a; Fukao & Bailey-Serres 2008b; Jung et al. 2009;

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Hattori et al. 2009; Hattori et al. 2011; Fukao et al. 2011; Pucciariello & Perata 2012; Dai et al. 2012).

Considering that rice (Oryza sativa L.) is an aerobic organism, its submergence for a long time may be fatal. Regulatory network of ET, the primary hormone in plants known to drive internode elongation under water surface, is deemed to be involved in the response of rice to submergence (Dai et al. 2012). A full understanding of the mechanism(s) controlling the ET signaling pathway in rice may greatly help rice survive under flooding conditions.

There are a number of studies about mathematical modeling of plant signaling networks (Espinosa-Sotto et al. 2004; Li et al. 2006; Sankar et al. 2011; Middleton et al. 2012; Beguerisse-Diaz et al. 2012). These studies have implemented three mathematical modeling formalisms, namely logical modeling, mechanistic ordinary differential equation (ODE) modeling, and logic-based ODE modeling.

Logical models are the simplest and are used to describe basic input–output behavior of the system. Moreover, these models provide qualitative information about the network's global dynamics. On the contrary, ODEs give a comprehensive quantitative analysis of the network's dynamics. However, the use of ODEs requires sufficient knowledge about the system's biological processes and kinetic information. This requirement limits its applicability to small networks. Logic-based ODEs are logical models transformed into a system of ODEs that are used to elaborate and predict system's behavior despite missing detailed mechanistic information (Muraro et al. 2012).

In this study, we opted to analyze the submergence regulatory network in rice using continuous logical modeling. This modeling approach was established by Mendoza & Xenarios (2006) and was characterized as a logic-based ODE type of modeling. Furthermore, this study contributes to the inclusion of possible extensions of the connections on current submergence model in rice presented in the studies of Fukao & Bailey-Serres (2008b), Bailey-Serres & Voesenek (2010), and Dai et al. (2012). This study is likely the first to describe the submergence regulatory network involving ET, GA and ABA, using the continuous logical modeling framework.

METHODOLOGY

Construction of Crosstalk Model of GA, ET and ABA During SubmergenceThe first part of the methodology is the detailed construction of the submergence regulatory network

in rice involving GA, ET and ABA. Various recent studies were used to establish the extensions between the connections among the different components of the network.

Construction of the Core Network The studies by Fukao & Bailey-Serres (2008b), Bailey-Serres & Voesenek (2010), and Dai et al. (2012) provided an overview of the submergence regulatory network in rice, depicting the involvement of the plant hormones ET, GA, and ABA in the response mechanism of plant adaptation to flooding and submergence. The level of ET essentially escalates during the time of submergence in water. ET then downregulates ABA, which has a positive effect on GA, a hormone that promotes the elongation of plant internodes (Dai et al. 2012).

There are several identified flood response genes responsive to ET. According to Hattori et al. (2009), SNORKEL1 (SK1) and SNORKEL2 (SK2) are the genes responsible for the activation of deep water response of rice. Under submergence, ET is upregulated in the internodes of plants, leading to significant expression of SK1 and SK2. These genes have nuclear localization signal and a single APETALA2/ETHYLENE RESPONSE FACTOR (ERF) domain. Thus, the SK genes belong to the ERF subfamily and are commonly expressed in leaves and stems (Hattori et al. 2009).

SUBMERGENCE 1A (SUB1A) is another submergence tolerance gene that encodes an ERF, but unlike SK genes, it inhibits plant elongation during flooding (Hattori et al. 2009; Bailey-Serres & Voesenek 2010; Dai et al. 2012). Moreover, Hattori et al. (2009) indicated that the presence of SUB1A in plants prevents the utilization of energy responsible for elongation, which leads to stunted growth. Although plants may survive in water for a couple of weeks, growth response can be activated only when flood regresses. SUB1A is a negative regulator of GA that promotes accumulation of SLENDER RICE 1 (SLR1) and SLR1 LIKE-1 (SLRL1) transcripts. GA responses are inhibited by SUB1A through the restriction of DELLA proteins (i.e., SLR1 and SLRL1) and their degradation in shoots submerged in water (Bailey-Serres & Voesenek 2010; Dai et al. 2012). Furthermore, Fukao & Bailey-Serres (2008b) reported that ABA has a negative effect on SUB1A, which restrains ET production.

ET-triggered, submergence-induced GA responsiveness acts as a positive regulator of SUBMERGENCE 1C (SUB1C). SUB1C acts as an upregulator of amylase, which converts starch into glucose needed to produce ATP for shoot elongation (Bailey-Serres & Voesenek 2010). Additionally, SUB1C is partially inhibited by SUB1A (Perata & Voesenek 2007; Bailey-Serres &

Nazareno et al: Logical Modeling of a Regulatory Network in Rice

Philippine Journal of ScienceVol. 146 No. 1, March 2017

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Voesenek 2010). Figure 1 shows the core network of the submergence regulatory network in rice adopted from the works of Fukao & Bailey-Serres (2008b), Bailey-Serres & Voesenek (2010), and Dai et al. (2012). The core network was reconstructed by elaborating the connections between ET and SUB1A, between ET and ABA, and between GA and ABA. We used various studies to establish these connections.

Connection Between ET and SUB1AA number of the core components of ET signaling have been known in Arabidopsis. These components include membrane receptors, namely ETHYLENE RESPONSE

Figure 1. Core network model of submergence regulatory network in rice.

1 (ETR1), ETHYLENE RESPONSE 2 (ETR2), ETHYLENE SENSOR 1 (ERS1), ETHYLENE SENSOR 2 (ERS2) and ETHYLENE INSENSITIVE 4 (EIN4) (Yoo et al. 2009), to nuclear activators. These membrane receptors bind to ET via an N-terminal domain in the endoplasmic reticulum. The absence of ET makes the receptors active, which leads to the negative regulation of ET signaling through the activation of CONSTITUTIVE TRIPLE RESPONSE 1 (CTR1). CTR1 encodes a putative Raf-like mitogen-activated protein kinase (MAPK), but when the receptors bind with ET, CTR1 is inactivated (Yoo et al. 2009). ETR1- or ERS1-associated CTR1 has been suspected to have a significant role in the inhibition



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of ET signaling process. It is still unclear how CTR1 and ETHYLENE-INSENSITIVE3 (EIN3)/EIN3-Like 1 (EIL1) are connected (Yoo et al. 2009). Yoo et al. (2009) postulated that, in the absence of ET, CTR1 directly or indirectly downregulates MKK9–MPK3 and -6 and mediates downstream MAPKs for the phosphorylation of T592, which helps degrade EIN3. On the other hand, when ET is present, MKK9–MPK3 and -6 becomes active for the phosphorylation of T174, which promotes EIN3 (Yoo et al. 2008).

ETHYLENE INSENSITIVE 2 (EIN2), which is located below CTR1 in the network, is known for being a genetic screen for ET insensitivity. Wang et al. (2013) reported that EIN2 could regulate the production of the transcription factor EIN3/EIL1 located in the nucleus, although the mechanism is not known. CTR1 prevents the nuclear localization of EIN2 through the phosphorylation of its C-terminal domain. The component EIN3/EIL1 undergoes degradation through F-box proteins EIN3-BINDING OF F-BOX 1 and 2 (EBF1/EBF2) (Yoo et al. 2009; Ju et al. 2012; Wang et al. 2013). EIN3 acts as a positive regulator of ET signaling by controlling the level of ETHYLENE RESPONSE FACTOR 1 (ERF1) through its binding to particular sequences of the ERF1 promoter (Wang et al. 2013).

ERFs are transcription factors that are plant specific. They contain a highly conserved domain having 58 or 59 amino acids that bind mainly to the GCC box area. They are located downstream in the ET regulatory network and are responsible for the stimulation of ET and stress responses. These ERFs have important involvement in various processes of plant development and stress responses, e.g. water submergence tolerance in the case of SK1 and SUB1A (Kohli & Screenivasulu 2013; Wang et al. 2013).

Interaction Between ET and ABAChen et al. (2010) presented a schematic diagram of the ET signaling pathway in the induced petiole elongation of Rumex accessions during submergence. Upon submergence, the level of ET increases resulting in a decrease in ABA biosynthesis level (Arc et al. 2013). Furthermore, there is activation of ABA catabolism via its degradation through the ABA 8′ hydroxylase pathway (Chen et al. 2010).

GA Signaling Pathway and Its Relationship with ABA GA plays an important role in plant growth. It is responsible for developmental processes such as seed germination, leaf expansion, stem elongation and flowering (Middleton et al. 2012, Golldack et al. 2013). The binding of cellular GA to the receptor GA-INSENSITIVE DWARF 1

(GID1) initializes GA signaling. The resulting complex GA-GID1 binds with the DELLA proteins, which are polyubiquitinated by the SCFSLY1/GID2 ubiquitin E3 ligase complex. Upon ubiquitination, DELLA proteins are degraded through the 26S proteasome pathway and activation of GA responses (e.g., stem elongation) takes place (Middleton et al. 2012; Golldack et al. 2013).

Additional and hypothesized connection interactions, such as the regulation of DELLA via posttranslational O-GlcNAcylation by SPINDLY (SPY), as well as phosphorylation by casein kinase, have been suggested by Golldack et al. (2013). In addition, DELLA proteins facilitate transcriptional activation of GA20ox and GA3ox genes necessary for the biosynthesis of GA (Middleton et al. 2012). Aside from these two genes, DELLA proteins modulate XERICO, a RING-H2 zinc-finger protein. This modulation increases cellular ABA levels through its biosynthesis pathway (Golldack et al. 2013).

Table 1 shows the summary interaction of the different components of the network. It also includes the notation used, which is summarized in Table 2. The reconstructed network showing the crosstalk of the three main phytohormones used for logical modeling in this study is shown in Figure 2. The core components are shown as green boxes while the dark blue boxes, blue box and red boxes are the additional components for ET–SUB1A connection, ET–ABA connection, and ABA–GA connection, respectively. Broken lines represent postulated pathways taken from various studies.

Implementation of Continuous Logical Modeling FrameworkMathematical analysis of the reconstructed network was implemented using continuous logical modeling, a method used in understanding signaling networks. Information about these signaling networks is usually qualitative, which makes it ideal for the implementation of logical modeling in the analysis. Logical models are used to describe biological system qualitatively and do dynamic simulation despite the lack of kinetic data or stoichiometric information for a given network system (Mendoza & Xenarios 2006). Mendoza & Xenarios (2006) applied the method in the regulatory network that controls the differentiation process of T helper cells. They were able to find the stable steady states by employing both discrete and continuous dynamical systems modelling. Sankar et al. (2011) adopted this method in order to develop a qualitative model for the interaction between auxin and brassinosteroid signaling pathways.

Boolean modeling has been used in analyzing gene regulatory networks by giving each component of the network a certain value describing its level of activation



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Figure 2. Reconstructed ethylene signalling network during water submergence.

Table 1. Summary interaction of the different components of the network.

Reaction Type Source Target Notation Reference/s

Activation submergence ET Bailey-Serres & Voesenek 2010; Dai et al. 2012

Inhibition ET ABA Bailey-Serres & Voesenek 2010; Dai et al. 2012

Inhibition ABA GA Bailey-Serres & Voesenek 2010; Dai et al. 2012

Activation ET SK1/SK2 Hattori et al. 2009; Bailey-Serres & Voesenek 2010

Activation SK1/SK2 GA Bailey-Serres & Voesenek 2010

Activation ET SUB1A Hattori et al. 2009; Bailey-Serres & Voesenek 2010

Activation SUB1A SLR1/SLRL1 Bailey-Serres & Voesenek 2010



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Inhibition SLR1/SLRL1 GA Bailey-Serres & Voesenek 2010; Dai et al. 2012

Activation GA elongation Bailey-Serres & Voesenek 2010;Middleton et al. 2012; Golldack et al. 2013

Inhibition ABA SUB1A Fukao & Bailey-Serres 2008b

Inhibition SUB1A ET Fukao & Bailey-Serres 2008b; Bailey-Serres & Voesenek 2010

Inhibition SUB1A SUB1C Perata & Voesenek 2007; Bailey-Serres & Voesenek 2010

Activation GA SUB1C Bailey-Serres & Voesenek 2010

Activation SUB1C amylase Bailey-Serres & Voesenek 2010

Activation amylase starch Bailey-Serres & Voesenek 2010

Activation starch glucose Bailey-Serres & Voesenek 2010

Activation glucose ATP Bailey-Serres & Voesenek 2010

Activation ATP elongation Bailey-Serres & Voesenek 2010

Activation ET ET-ETR1 complex Yoo et al. 2009

Activation ETR1 ET-ETR1 complex Yoo et al. 2009

Activation ETR1 CTR1 Yoo et al. 2009

Inhibition ET-ETR1 complex CTR1 Yoo et al. 2009

Inhibition CTR1 MKK9–MPK3 and -6 Yoo et al. 2009

Inhibition CTR1 EIN3/EIL1 Yoo et al. 2008

Activation CTR1 EIN2 Wang et al. 2013

Activation MKK9–MPK3 and -6 EIN3/EIL1 Yoo et al. 2008

Activation EIN2 EIN3/ EIL1 Wang et al. 2013

Inhibition EBF1/EBF2 EIN3/EIL1 Yoo et al. 2009; Ju et al. 2012; Wang et al. 2013

Activation EIN3/EIL1 ERF1 Wang et al. 2013

Activation ERF1 SUB1A Kohli & Screenivasulu 2013; Wang et al. 2013;

Activation ET ABA catabolism Chen et al. 2010

Table 1 continuation . . .



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Inhibition ABA catabolism ABA Chen et al. 2010

Inhibition ET ABA biosynthesis Arc et al. 2013

Activation ABA biosynthesis ABA Chen et al. 2010

Inhibition ABA GA biosynthesis Dai et al. 2012

Activation GA biosynthesis GA Middleton et al. 2012

Activation GA GA-GID1 Middleton et al. 2012; Golldack et al. 2013

Activation GA-GID1 GA-GID1-DELLA Middleton et al. 2012; Golldack et al. 2013

Activation GA-GID1-DELLA DELLA-UB Middleton et al. 2012; Golldack et al. 2013

Activation DELLA-UB DELLA degraded Middleton et al. 2012; Golldack et al. 2013

Activation DELLA degraded elongation Middleton et al. 2012; Golldack et al. 2013

Inhibition SLR1/SLRL1 elongation Middleton et al. 2012

Activation SPY1 SLR1/SLRL1 Golldack et al. 2013

Activation casein kinase SLR1/SLRL1 Golldack et al. 2013

Activation SLR1/SLRL1 GA20ox Middleton et al. 2012

Activation SLR1/SLRL1 GA3ox Middleton et al. 2012

Activation SLR1/SLRL1 XERICO Golldack et al. 2013

Activation XERICO ABA biosynthesis Golldack et al. 2013

Table 2. Notations used for the ethylene signaling network during water submergence.

Notation Name

X1 submergence level

X2 ET

X3 ET-ETR1

X4 ETR1

X5 CTR1

X6 MKK9–MPK3 and -6

X7 EIN2

X8 EIN3/EIL1

X9 EBF1/EBF2


or inactivation. A value of 1 is given for active component and a value of 0 is given for inactive component of the network. However, this formalism is somewhat discrete and lacks timescale. Mendoza & Xenarios (2006) proposed a standard method of transforming the discrete dynamical system into a continuous system model. The first step is to convert the network into a discrete dynamical system wherein all the stable steady states are obtained for the discrete system. These steady states were used as initial conditions to solve the continuous dynamical system. The schematic representation of this method has been illustrated in Mendoza & Xenarios (2006).

The following set of ODEs was used to describe the network as a continuous dynamical system:



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X10ERF1

X11SK1/SK2

X12SUB1A

X13SLR1/SLRL1

X14SUB1C

X15amylase

X16starch

X17glucose

X18ATP

X19ABA catabolism

X20ABA

X21ABA biosynthesis

X22GA

X23GA-GID1

X24GA-GID1-DELLA

X25DELLA-UB

X26DELLA degraded

X28SPY1

X29caseine kinase

X30GA biosynthesis

X31GA20ox

X32GA3ox

X33XERICO

X34elongation


Let { }anx be a set of activators and { }i

mx be a set of

inhibitors of ix , for every species ix . Then

(1)

(2)

* use if ix has both activators and inhibitors

** use if ix has activators only

*** use if ix has inhibitors only

Each differential equation indicated an activation and a decay term. The activation is a sigmoidal function of ω associated to the total input to the node while the decay is directly proportional to the level of activation

of the node. The parameter h is a gain of the activation function that controls the slope of the curve. The function ω is characterized in three forms incorporating the effect of activators and inhibitors to a particular network component. The parameters a and b are the weights of activators and inhibitors, respectively. The values of the variables and parameters are described as follows:

0 1ix≤ ≤ , 0 1iω≤ ≤ , h , nα , mβ , and 0iγ >. The value of node is within the interval [0,1]. This indicates that the level of activation is normalized and not an absolute value (Mendoza & Xenarios 2006).

The continuous dynamical system was formulated using the formalism established by Mendoza & Xenarios (2006). There is a total of 28 differential equations associated with the mechanism of the regulatory network. These equations are as follows:

(3)

These differential equations are solved using a software package called Berkeley Madonna (Macey & Oster 2001). The initial conditions used were obtained from the steady state solution of the discrete dynamical system obtained from Version 2.3.1 of GINsim (2016) software package. Since the solution was trivial, the initial activation levels of the involved components were all set to 0. The

parameters α , β and γ have values all set to 1, while h = 10. These are specified values taken from the published work of Mendoza & Xenarios (2006).

RESULTS AND DISCUSSIONThe results indicated that majority of the components of the submergence regulatory system, along with the elongation response node, had oscillatory but periodic behavior. This finding is consistent with the notion of inherent buffering in signaling networks. According to Sankar et al. (2011), buffering is an important mechanism



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for developmental flexibility since it deters the system from being in a situation of signaling lock-in and from having an exaggerated response to transient stimulus.

There are 33 nodes in the network in which only 28 components are represented by differential equations derived from the logical modeling formalism. As shown in Figure 3, only 23 components were activated in the whole running time (t = 50 with step size of 0.01). ET, ET-ETR1 complex, CTR1, MKK9–MPK3 and -6, and ABA catabolism nodes were not activated. This might be attributed to the deactivation of ET, submergence level (in the case of ABA catabolism), and ETR1 (in the case of CTR1). Almost all the remaining components exhibited a periodic behavior. The components EIN2 and EIN3/EIL1 were the first to be activated in the system.

Figure 4 depicts the activation levels of SLR1/SLRL1, ABA, GA, and elongation. The components SLR1/SLRL1 as a repressor of GA signaling, component ABA as a repressor of GA biosynthesis, and component GA as the key growth hormone are important in the elongation response of plants. As shown in Figure 4, GA has a very small amplitude and always has a high level of activation. Moreover, the DELLA protein SLR1/SLRL1 acts as a main regulator in the elongation process. When the level of SLR1/SLRL1 achieved its peak, the elongation level suddenly dropped. This is consistent with the mechanism of SLR1/SLRL1 proteins inhibiting GA-induced growth responses in rice. It is evident that the behavior of most of the components is oscillatory and periodic in all the simulations at different levels of submergence. This is consistent with the behavior exhibited under normal condition. However, ET level started to be expressed

Figure 3. Behavior of each component at normal condition.

and continuously increased its peak as the submergence level rose. Subsequently, ABA catabolism is activated and its peak increased as the submergence escalated. This observation is expected since ET is an inhibitor of ABA; an increase in ET will result in a decrease in the ABA biosynthesis level (Arc et al. 2013). Activation of ABA catabolism would cause degradation of ABA via the ABA 8′ hydroxylase pathway (Fukao & Bailey-Serres 2008a; Chen et al. 2010). The model can also be described as robust since the behavior of the system does not change as the level of submergence varies.

The activation level of all of the components at normal condition was periodic at different submergence levels, except EIN2, ERF1, SK1/SK2, DELLA-UB and DELLA degraded, which seemed to stabilize. It is also evident that ET, ET-ETR1, and MKK9–MPK3 and -6, as well as ABA catabolism, had similar pattern of behavior. Cluster could then be formed according to the pattern of behavior exhibited by each component. The clusters that can be considered are amylase and starch; GA and GA-GID1-DELLA; GA20ox, GA3ox and XERICO; ABA and ABA biosynthesis; glucose and ATP; and SUB1A, SLR1/SLRL1 and SUB1C. This clustering can be related to their immediate connection with each other and the complexity of influences a component received.

The activation level of ET was periodic for all variations in the submergence levels. The peak of the graph became higher as the level of submergence rose. It achieved its highest peak (0.82516589) when the level is equal to 1. The most significant level surge occurred when the submergence level was changed from 0.1 to 0.2. The GA levels at different submergence levels are consistently high



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Figure 4. ABA, SLR1/SLRL1, GA and Elongation activation levels behavior at normal condition.

despite the oscillatory behavior. It achieved its highest activation peak (0.98998697) when the submergence level is 1. This is a significant finding since GA is the key element for the activation of growth in plants. SLR1/SLR1 expression was limited to some level (around 0.75) and its highest peak (0.75550733) could be observed when the submergence level is 1. The limiting aspect can be associated to its high dependence on SUB1A. Both SPY2 and casein kinase are deactivated in the whole simulation run. It is notable that the increase in the level of submergence had a negative effect on the activation levels of ABA. There was a decreasing trend for the peak of ABA levels. It registered a minimum peak of 0.82968031 and this happened when the submergence level is 1.

An important result of this model is the prediction of the significant role of SUB1A in the sustained oscillatory behavior of ET. ET activated SUB1A through this pathway: ETET–ETR1→CTR1MKK9–MPK3 and–6EIN3/EIL1ERF1SUB1A

However, SUB1A inhibited ET at the same time. This simple positive–negative feedback loop of interacting genes or proteins has the potential to generate sustained oscillations. When the negative feedback from SUB1A was removed from the system, at normal condition (i.e. submergence level = 0), it would result into an oscillatory system. However, when ET was introduced, stability of the components, including ET, is possible.

The prominent oscillatory behavior of the system under submerged and non-submerged conditions may be attributed to the possible oscillatory accumulation of SUB1A mRNA in rice. According to the study of Peña-Castro et al. (2011), this oscillation was observed every 12 hours for both conditions. Although this phenomenon

is not common in plants, this might be an indication of SUB1A regulation in response to various stimuli. In fact, microarray analysis has shown that there is an interaction between clock and the different hormone signaling (e.g. ET) (Robertson et al. 2008).

SUMMARY AND CONCLUSIONA total of 28 differential equations were considered in the continuous logical modeling. The result is consistent with the inherent buffering of signaling pathways since majority of the components showed a periodic behavior. Other notable finding is the key role of the DELLA protein SLR1/SLRL1 in the regulation of GA-induced growth in rice.

The introduction of submergence in the system confirmed its positive effect on ET. The activation level of all of the components is periodic at different submergence levels, except that of EIN2, ERF1, SK1/SK2, DELLA-UB, and DELLA degraded. Clusters based on the pattern of behavior exhibited by each component were formed. For instance, amylase and starch; GA and GA-GID1-DELLA; GA20ox, GA3ox, and XERICO; ABA and ABA biosynthesis; glucose and ATP; and SUB1A, SLR1/SLRL1; and SUB1C can be considered as clusters. This clustering can be related to their immediate connection with each other and the complexity of influences a component receives. Lastly, SUB1A has been shown to play an important role in the continued oscillatory behavior of ET under submergence.



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